|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}{y^{\prime \prime }}^{2}-x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.367 |
|
|
\[
{}{y^{\prime \prime }}^{3} = 12 y^{\prime } \left (x y^{\prime \prime }-2 y^{\prime }\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
8.104 |
|
|
\[
{}3 y y^{\prime } y^{\prime \prime } = {y^{\prime }}^{3}-1
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
4.646 |
|
|
\[
{}4 y {y^{\prime }}^{2} y^{\prime \prime } = {y^{\prime }}^{4}+3
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
3.549 |
|
|
\[
{}y^{\prime \prime }+y = -\cos \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.978 |
|
|
\[
{}y^{\prime \prime }-6 y^{\prime }+9 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.049 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = 12 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.111 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime }+2 y = x^{2}+2 x +1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.069 |
|
|
\[
{}x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+4 = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
4.847 |
|
|
\[
{}6 x {y^{\prime }}^{2}-\left (3 x +2 y\right ) y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
2.054 |
|
|
\[
{}9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
80.571 |
|
|
\[
{}4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.520 |
|
|
\[
{}x^{6} {y^{\prime }}^{2}-2 x y^{\prime }-4 y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.263 |
|
|
\[
{}5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.480 |
|
|
\[
{}y^{2} {y^{\prime }}^{2}-y \left (x +1\right ) y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
4.117 |
|
|
\[
{}4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9 = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
5.934 |
|
|
\[
{}4 y^{2} {y^{\prime }}^{3}-2 x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
105.388 |
|
|
\[
{}{y^{\prime }}^{4}+x y^{\prime }-3 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
2.277 |
|
|
\[
{}x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
2.296 |
|
|
\[
{}16 x {y^{\prime }}^{2}+8 y^{\prime } y+y^{6} = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.481 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (x^{2}+1\right ) y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
0.522 |
|
|
\[
{}{y^{\prime }}^{3}-2 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.204 |
|
|
\[
{}9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-1 = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
23.071 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-\left (2 x y+1\right ) y^{\prime }+y^{2}+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.650 |
|
|
\[
{}x^{6} {y^{\prime }}^{2} = 16 y+8 x y^{\prime }
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.173 |
|
|
\[
{}x^{2} {y^{\prime }}^{2} = \left (x -y\right )^{2}
\] |
[_linear] |
✓ |
2.949 |
|
|
\[
{}\left (y^{\prime }+1\right )^{2} \left (y-x y^{\prime }\right ) = 1
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
1.001 |
|
|
\[
{}{y^{\prime }}^{3}-{y^{\prime }}^{2}+x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.688 |
|
|
\[
{}x {y^{\prime }}^{2}+y \left (1-x \right ) y^{\prime }-y^{2} = 0
\] |
[_quadrature] |
✓ |
2.470 |
|
|
\[
{}y {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.900 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (k -x -y\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.589 |
|
|
\[
{}x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
131.250 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.344 |
|
|
\[
{}y^{\prime \prime }-9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.566 |
|
|
\[
{}y^{\prime \prime }+3 x y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.621 |
|
|
\[
{}\left (4 x^{2}+1\right ) y^{\prime \prime }-8 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.619 |
|
|
\[
{}\left (-4 x^{2}+1\right ) y^{\prime \prime }+8 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.649 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.507 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+10 x y^{\prime }+20 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.680 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }+2 x y^{\prime }-12 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.660 |
|
|
\[
{}\left (x^{2}-9\right ) y^{\prime \prime }+3 x y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.631 |
|
|
\[
{}y^{\prime \prime }+2 x y^{\prime }+5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.618 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }+6 x y^{\prime }+4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.686 |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }-5 x y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.661 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.510 |
|
|
\[
{}\left (-4 x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }-4 y = 0
\] |
[_Gegenbauer] |
✓ |
0.691 |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.630 |
|
|
\[
{}y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0
\] |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✗ |
0.079 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+3 y = x^{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.651 |
|
|
\[
{}y^{\prime \prime }+2 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.622 |
|
|
\[
{}y^{\prime \prime }+3 x y^{\prime }+7 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.630 |
|
|
\[
{}2 y^{\prime \prime }+9 x y^{\prime }-36 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.617 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }-9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.650 |
|
|
\[
{}\left (x^{2}+4\right ) y^{\prime \prime }+3 x y^{\prime }-8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.648 |
|
|
\[
{}\left (9 x^{2}+1\right ) y^{\prime \prime }-18 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.635 |
|
|
\[
{}\left (3 x^{2}+1\right ) y^{\prime \prime }+13 x y^{\prime }+7 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.689 |
|
|
\[
{}\left (2 x^{2}+1\right ) y^{\prime \prime }+11 x y^{\prime }+9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.697 |
|
|
\[
{}y^{\prime \prime }-2 \left (x +3\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.659 |
|
|
\[
{}y^{\prime \prime }+\left (-2+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.543 |
|
|
\[
{}\left (x^{2}-2 x +2\right ) y^{\prime \prime }-4 \left (x -1\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.534 |
|
|
\[
{}2 x \left (x +1\right ) y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.016 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.987 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x y^{\prime }-\left (4 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.931 |
|
|
\[
{}4 x y^{\prime \prime }+3 y^{\prime }+3 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.063 |
|
|
\[
{}2 \left (1-x \right ) x^{2} y^{\prime \prime }-x \left (1+7 x \right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.135 |
|
|
\[
{}2 x y^{\prime \prime }+5 \left (-2 x +1\right ) y^{\prime }-5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.083 |
|
|
\[
{}8 x^{2} y^{\prime \prime }+10 x y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.122 |
|
|
\[
{}2 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.875 |
|
|
\[
{}2 x \left (x +3\right ) y^{\prime \prime }-3 \left (x +1\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.053 |
|
|
\[
{}2 x y^{\prime \prime }+\left (-2 x^{2}+1\right ) y^{\prime }-4 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.906 |
|
|
\[
{}x \left (4-x \right ) y^{\prime \prime }+\left (2-x \right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.132 |
|
|
\[
{}3 x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.109 |
|
|
\[
{}2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.049 |
|
|
\[
{}2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-5 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.113 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 x \left (1-x \right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.127 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x \left (4 x -1\right ) y^{\prime }+2 \left (3 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.086 |
|
|
\[
{}2 x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.843 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.789 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.798 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.784 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.807 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.150 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.175 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.719 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.064 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.976 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.960 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.142 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.151 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 x y^{\prime }+5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.971 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-8 x y^{\prime }+8 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.127 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.949 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (-2 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.965 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.919 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (4 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.880 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.861 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (3 x +1\right ) y^{\prime }+\left (1-6 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.968 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x -1\right ) y^{\prime }+\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.934 |
|
|
\[
{}x \left (-2+x \right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.880 |
|
|
\[
{}x \left (-2+x \right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.900 |
|